Abstract
In this paper, we study an interesting generalization of standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces due to the recent work of Jleli and Samet. Here we modify the result for Ciric quasi-contraction-type mappings and also prove the same result by taking D-admissible mappings. Moreover, we establish fixed point theorems for two well-known nonlinear contractions like rational contraction mappings and Wardowski type contraction mappings. Several important results in the literature can be derived from our results. Suitable examples are presented to substantiate our obtained results.
Highlights
1 Introduction Metric fixed point theory plays a crucial role in the field of functional analysis
We investigate the existence and uniqueness of a fixed point for the mappings satisfying nonlinear rational contraction and Wardowski type F-contraction, where the function F is taken from a more general class of functions than that known in the existing literature
We prove a fixed point theorem for rational contraction type mappings
Summary
Metric fixed point theory plays a crucial role in the field of functional analysis. It was first introduced by the great Polish mathematician Banach [ ]. (X, D) is said to be a generalized metric space if the following conditions are satisfied: (D ) ∀x, y ∈ X, D(x, y) = ⇒ x = y; (D ) ∀x, y ∈ X, D(x, y) = D(y, x); (D ) there exists c > such that for all (x, y) ∈ X × X and (xn) ∈ C(D, X, x), D(x, y) ≤ c lim sup D(xn, y).
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